The present invention relates to the logging of boreholes to determine the fluid contents of rock formations penetrated by a borehole. In particular, the invention relates to electric or resistivity logging devices used to determine the resistivities of porous rock formations in order to distinguish water bearing zones from hydrocarbon bearing zones. In the case of high resistivity formations containing low salinity of fresh water there may not exist sufficient contrast in the fluid resistivities to permit evaluation of the zones of interest on the basis of resistivity measurements. This problem has led to the use of induction logging devices in an attempt to measure the dielectric constants of the rock formations surrounding the borehole. The dielectric constant of water is large compared to that of hydrocarbons and therefore one can distinguish a fresh water bearing zone from a hydrocarbon bearing zone from a knowledge of the dielectric constant of the zone. Presently used or conventional induction logging devices operate at a frequency of 20 kHz. These devices determine an apparent resistivity of the formation surrounding the borehole by utilizing the component of the voltage induced in a measuring coil which oscillates in-phase with respect to the alternating current in the transmitter coil. Conventional induction logging devices have the same problems as all conventional electrical logging devices in distinguishing between two highly resistive zones, one of which contains fresh water and the other which contains hydrocarbons. A useful reference to the theory underlying the operation of conventional induction logging devices is the publication by J. H. Moran and K. S. Kunz entitled "Basic Theory of Induction Logging and Application to Study of Two-Coil Sondes" which is published in Geophysics, vol. 27, no. 6, pp. 829-858, 1962.
In an attempt to overcome the above problems experienced by conventional resistivity logging devices, U.S. Pat. No. 4,012,689 suggests the use of radio frequencies in the range of 20 to 40 MHz and proposes a method for determining both the dielectric constant and resistivity of the formation surrounding the borehole. The use of higher frequencies is necessary in order to obtain a tool response which is sensitive to the dielectric constant of the formation. This can be understood in more detail by comparing the relative magnitudes of the conduction current and the displacement current (the dielectric constant enters the equations through this term) terms in Maxwell's equations. For the dielectric constants and resistivities encountered in well logging these two terms become of comparable magnitude in the frequency range proposed in the above referenced patent. At the lower frequencies at which conventional induction logging devices operate, the displacement current term is negligible compared to the conduction current term and therefore the response of these devices is insensitive to the dielectric constant. The above referenced patent defines the response of the proposed device in terms of the phase shift between the signals received at two spatially separated receiver coils and the signal amplitude at one of the receiver coils with respect to the amplitude of the same signal in air. This patent provides a theoretically calculated nomogram (e.g., see FIG. 6 of the patent) for the case of a logging sonde in an infinite homogeneous medium penetrated by a borehole. For this logging geometry and for the specific borehole properties (e.g., drilling mud resistivity and borehole radius) for which this nomogram is valid one can use the measured phase shift and signal amplitude as known quantities and thereby determine, from the nomogram, values of the resistivity and dielectric constant of the formation surrounding the borehole.
The method proposed in the above referenced patent for determining the formation resistivity and dielectric constant has some serious problems. These problems can be traced to the fact that the signal amplitude (relative to its value in air) at a receiver coil is extremely sensitive to the properties of the borehole. To illustrate the implications of this, we consider the nomogram (FIG. 6) in the above referenced patent. This nomogram is valid for a fresh water mud having resistivity of 1 ohm-m. If a salt water mud having a resistivity of 0.0667 ohm-m is used instead then the values of the amplitudes shown on the nomogram are in error by a factor of roughly 100. The amplitude is also very sensitive to the borehole radius whenever the drilling mud is very conductive. For example, if the borehole is filled with a drilling mud having resistivity 0.0667 ohm-m and the borehole radius is increased from 0.1 m to 0.127 m then the signal amplitudes at a receiver coil decrease by roughly a factor of 10. Thus small variations in mud resistivity and borehole size from those assumed in preparing the nomogram can make the results meaningless. In addition to the above problems the patent makes no reference to the problem created by the invasion of the drilling mud into the formation surrounding the borehole. The mud invasion can have a serious effect on the accuracy of the results obtained using the proposed method since the invaded zone has a different dielectric constant and resistivity than the non-invaded formation.